Is this normal?

My 11 month old daughter has been consistently wanting to sleep most of the day. I'll get her up at 9 am, and within an hour she is tired again and cranky. She has literally fallen asleep in her highchair. She is 2 days away from her first birthday. She wakes up late at night and will just play in her bed, sometimes quietly, sometimes loudly for an hour or two. I don't go into her unless she is crying. Is this wanting to sleep during the day have anything to do with her being awake at night? Or is it a growth spurt?